And so it begins. When Senator Saxby Chambliss announced last week that he no longer considered himself bound by a no-new-taxes pledge he signed two decades ago, the Georgia Republican made an important break with a GOP article of faith — an early sign that compromise could yet be possible in the coming weeks and months.

And maybe years. Endorsed by Senator Lindsey Graham of South Carolina and by Representative Peter King of New York, the Chambliss decision — one that put him on the other side of Grover Norquist and the conservative base — is reminiscent of what began happening among Democrats in the aftermath of the 1984 Reagan landslide. Old allegiances to traditional Democratic constituencies were re-examined; the Democratic Leadership Council (DLC) urged office holders and candidates to adopt centrist rhetoric and a promarket orientation.

It worked. In the 1990s Bill Clinton became the first two-term Democratic president since FDR, and Al Gore — another early DLCer — won the popular vote in 2000. The climatic moment of the New Democrat ascendancy came in 1996, when Clinton declared that “the era of big government” was over.

Republicans are overdue for their own rethinking. After the exhaustion of the first decade of the new century, it’s understandable that such self-examination has been slow in coming, but it apparently has finally come. Whether the GOP is to be pragmatic in the mold of George H.W. Bush or more ideological in the mode of his son is a live question. The Chambliss-Graham-King moment suggests the debate is very much on.

In the short and medium term, President Obama may be able to take advantage of the fluid opinion within the GOP to get a lasting fiscal deal. In the long term, the kind of party the Republicans choose to be will help define our politics as surely as the rise of the New Democrats did.